Introduction¶
Cancer Progression Models¶
Cancer is an heterogeneous disease caused by the continuous accumulation of somatic mutations during lifetime of an individual. Somatic mutations that affect the cells are divided in:
- Passenger mutations --> Silent mutations
- Driver mutations --> Lead to cancer progression
Cancer Progression Models (cont.)¶
- Tumor samples are obtained as cross-sectional samples --> single-time snapshots from tumors
- Not all possible order in mutations are equally responsible for cancer progression --> infer order of accumulation of mutations leading to cancer progression. Order in accumulation of mutations is covered by Cancer Progression Models (CPM). They are depicted as Directed Acyclic Graphs (DAG), where nodes represent genes and arrows dependencies between them
Evolutionary Models¶
Order of restrictions are encoded in DAGs
Mutations occur only if the preceding parent mutations have occurred (monotonicity)
Genotypes can follow different paths during disease progression
Evolutionary tumor progression models allows deviations from monotonicity
Evolutionary Models (cont.)¶
- Fitness landscapes can be used to:
- Visualize the possible paths of tumor progression
- Identify genes that block those paths
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Order of effects¶
The order in which somatic mutations are acquired influence clonal evolution
- Mutations can behave as driver or passenger depending on the genetic context
Therefore, the fitness a mutations depends in which mutations were acquired previously
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Epistatic interactions¶
Cancer progression is driven by the accumulation of somatic mutations that interact epistatically
This is, their effect is non-additive to the tumor fitness as a phenotype
Synthetic Viability¶
- The combination of two mutations that rescue the lethal effects of a each single mutation
Mutual Exclusivity¶
- Common in cancer progresion: pathways
- Null effect: a mutation that occurs first produces the most selective advantage
Mutual Exclusivity (cont.)¶
- Synthetic lethality: combination of two mutations is detrimental for the viability of the cell, whereas each mutation is not
Frequency-dependent fitness¶
Coexistance of multiple clones in time
Evolutionary game theory
Fitness is actually a function of the relative frequency of other clones
PathTiMEx, a generative probabilistic graphical model of cancer progression.¶
PathTiMex is a probabilistic model of tumor progression among mutually exclusive driver pathways. This model was used to infer cancer progression in colorectal cancer.
This generative model is mapped into an evolutionary model, where deviations from monotonicity are allowed.
Model¶
In [4]:
## Restriction table (extended version of the poset)
colcancer <- data.frame(
parent = c(rep("Root",3), "A", "B", "C"), ## Parent nodes
child = c("A", "B", "D", "C", "E", "E"), ## Child nodes
s = c(0.5, 0.2, 0.05, 0.1, rep(0.05, 2)), ## Restrictions are satisfied
sh = -0.3, ## Deviations from monotonicity (penalization)
typeDep = "MN" ## Type of dependency
)
## Fitness specification of the poset
colcancer_efec <- allFitnessEffects(
colcancer, # Poset
geneToModule = c( ## Specification of the modules
"Root" = "Root",
"A" = "APC",
"B" = "TP53, EVC2",
"C" = "KRAS",
"D" = "PI3KCA, EPHA",
"E" = "FBXW7, TCF7L2"),
drvNames = c( ## Specification of drivers
"APC", "TP53", "EVC2", "KRAS",
"PI3KCA", "EPHA", "FBXW7", "TCF7L2"))
In [3]:
## DAG representation
plot(colcancer_efec, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Map Genotypes to Fitness¶
In [5]:
# Evaluation of all genotypes and its fitness
colcancer_efec_FL <- evalAllGenotypes(colcancer_efec, max = 110000)
## Plot of fitness landscape
plotFitnessLandscape(colcancer_efec_FL)
Order Effects in cancer progression¶
Simplified model with 4 genes: APC, TP53, FBXW7 and KRAS.
In [4]:
# DAG from the simplified model
plot(cc_visuali, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Order Effects in cancer progression (cont.)¶
Mutation's order is inferred with pathTiMEx through the waiting time rate parameter. It informs about the mutation's arise. Fitness value associated to each order is derived from this parameter.
| Gene/module | Waiting time rate parameter |
|---|---|
| APC | 9.5 |
| KRAS | 2.89 |
| TP53, EVC2 | 1.92 |
| PIK3CA, EPHA3 | 0.17 |
| FBXW7, TCF7L2 | 0.08 |
The order in mutations: APC > TP53 > KRAS > FBXW7 is consistent with restrictions and is associated to the highest fitness value. Different order deviates from monotoniciy and lower fitness is associated.
Order Effects in cancer progression (cont.)¶
In [5]:
## Order effects
cc_order <- allFitnessEffects(
orderEffects = c("A > B > C > D" = 0.5,
"B > A > C > D" = 0.2,
"B > C > A > D" = 0.1,
"B > C > D > A" = 0.05,
"A > C" = 0.2,
"C > A" = 0.05,
"D > A" = 0.05,
"A > D" = 0.2,
"B > D" = 0.2,
"C > D" = 0.2,
"B > C" = 0.2,
"C > B" = 0.1,
"B > A" = 0.1,
"A > B" = 0.3),
geneToModule =
c("A" = "APC",
"B" = "KRAS",
"C" = "TP53",
"D" = "FBXW7") )
Map Genotypes to Fitness¶
In [6]:
## Fitness associated to each genotype
(cc_order_geno <- evalAllGenotypes(cc_order, order = TRUE))
Map Genotypes to Fitness (cont.)¶
In [7]:
#DAG
plot(cc_order)
In [8]:
# Fitness landscape
plotFitnessLandscape(cc_order_geno)
Pathway Linear Progression Model¶
Generative probabilistic model
The order in which mutations arise are better described at the pathway level instead of a gene level
Model mapped the progression model from colorectal cancer data
Model¶
In [12]:
## Define poset restrictions, mapping of genes to modules, and driver genes
(CRC_W <- allFitnessEffects(data.frame(parent = c("Root", "A", "B", "C"),
child = c("A", "B", "C", "D"),
s = c(0.6, 0.4, 0.1, 0.05),
sh = -0.5,
typeDep = "MN"),
geneToModule = c("Root" = "Root",
"A" = "APC, EPHA3, TCF7L2",
"B" = "EVC2, PIK3CA, TP53",
"C" = "KRAS",
"D" = "FBXW7"),
drvNames = c("APC", "EPHA3", "TCF7L2", "EVC2", "PIK3CA",
"TP53", "KRAS", "FBXW7")))
DAG¶
In [6]:
# DAG representation
plot(CRC_W, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Map Genotypes to Fitness¶
In [13]:
## Map genotypes to fitness
CRC_F <- evalAllGenotypes(CRC_W, order = FALSE, addwt = TRUE)
## Plot of fitness landscape
plot(CRC_F)
Simplified model¶
In [14]:
## Simplified model
## Define poset restrictions, mapping of genes to modules, and driver genes
(CRC_W2 <- allFitnessEffects(data.frame(parent = c(rep("Root", 2), "A", "B", "C"),
child = c("A", "B", rep("C", 2), "D"),
s = c(0.2, 0.1, rep(0.05, 2), 0.01),
sh = -0.5,
typeDep = c(rep("XMPN", 4), "MN")),
geneToModule = c("Root" = "Root",
"A" = "APC",
"B" = "TP53",
"C" = "KRAS",
"D" = "FBXW7"),
drvNames = c("APC", "TP53", "KRAS", "FBXW7")))
In [3]:
# DAG representation
plot(CRC_W2, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Map Genotypes to Fitness¶
In [15]:
## Simplified Model
## Map genotypes to fitness
(CRC_F2 <- evalAllGenotypes(CRC_W2, order = FALSE, addwt = TRUE))
Map Genotypes to Fitness (cont.)¶
In [16]:
## Plot of fitness landscape
plot(CRC_F2, use_ggrepel = TRUE)
Synthetic Lethality via Three-way Interaction¶
Restrictions imposed with
XORFitness values that reflect slightly deleterious effect (if two genes appear)
or a highly deleterious effect (if three genes appear).
In [17]:
## Simplified model
## Define poset restrictions, mapping of genes to modules, and driver genes
(CRC_W4 <- allFitnessEffects(data.frame(parent = c(rep("Root", 2), "A", "B", "C"),
child = c("A", "B", rep("C", 2), "D"),
s = c(0.2, 0.1, rep(0.05, 2), 0.01),
sh = -0.5,
typeDep = c(rep("XMPN", 4), "MN")),
epistasis = c("A : -B : -C" = 0.2,
"-A : B : -C" = 0.1,
"-A : -B : C" = 0.05,
"A : B : -C" = 0.01,
"-A : B : C" = 0.02,
"-B : A : C" = 0.02,
"A : B : C" = -0.5),
geneToModule = c("Root" = "Root",
"A" = "APC",
"B" = "TP53",
"C" = "KRAS",
"D" = "FBXW7"),
drvNames = c("APC", "TP53", "KRAS", "FBXW7")))
In [3]:
# DAG representation
plot(CRC_W4, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Map Genotypes to Fitness¶
In [18]:
## Map genotypes to fitness
CRC_F2 <- evalAllGenotypes(CRC_W4, order = FALSE, addwt = TRUE)
(CRC_F2)
Map Genotypes to Fitness (cont.)¶
In [19]:
## Plot of fitness landscape
plot(CRC_F2, use_ggrepel = TRUE)
Synthetic Viability with a Three-way Interaction¶
Highly deleterious effects if APC, TP53, or KRAS appear independently
Slightly deleterious effects were set if two of those genes appear in a genotype
Benefitial effect for the genotype of the three genes
Restrictions imposed with
SM
In [20]:
## Simplified model
## SM because synthetic viability requires both parent nodes.
## Define poset restrictions, mapping of genes to modules, and driver genes
(CRC_W6 <- allFitnessEffects(data.frame(parent = c(rep("Root", 2), "A", "B", "C"),
child = c("A", "B", rep("C", 2), "D"),
s = c(0.2, 0.1, rep(0.05, 2), 0.01),
sh = -0.5,
typeDep = c(rep("MN", 5))),
epistasis = c("A : -B : -C" = -0.2,
"-A : B : -C" = -0.2,
"-A : -B : C" = -0.3,
"A : B : -C" = -0.05,
"-A : B : C" = -0.01,
"A : -B : C" = -0.01,
"A : B : C" = 0.5),
geneToModule = c("Root" = "Root",
"A" = "APC",
"B" = "TP53",
"C" = "KRAS",
"D" = "FBXW7"),
drvNames = c("APC", "TP53", "KRAS", "FBXW7")))
In [3]:
# DAG representation
plot(CRC_W6, expandModules = TRUE, autofit = TRUE, lwdf = 2)
Map Genotypes to Fitness¶
In [21]:
## Map genotypes to fitness
CRC_F4 <- evalAllGenotypes(CRC_W6, order = FALSE, addwt = TRUE)
(CRC_F4)
Map Genotypes to Fitness (cont.)¶
In [22]:
## Plot of fitness landscape
plot(CRC_F4, use_ggrepel = TRUE)
A Probabilistic Model of Mutually Exclusive Linearly Ordered Driver Pathways (Mohaghegh Neyshabouri et al.)¶
This model assumes driver genes are over-represented among those mutated across a large tumor collection and, thus, they can be identified in terms of frequency. Also, those participating of the same pathway are mutated in a mutually exclusive manner because more than one mutation in a pathway does not give any selective advantage to the clone. analyze one large dataset of colorectal adenocarcinoma (COADREAD) from IntOGen-mutations database.
Model¶
In [23]:
## Restriction table, including DAG of restrictions specifications and associated fitness
COADREAD_rT <- data.frame(
parent = c("Root", "A", "B", "C", "D", "E", "F"), # Parent nodes
child = c("A", "B", "C", "D", "E", "F", "G"), # Child nodes
s = 0.5,
sh = c(rep(-1, 4), rep(-.5, 2), -.2),
typeDep = "MN")
## Create fitness specifications from DAG of restrictions considering modules
COADREAD_fitness <- allFitnessEffects(
COADREAD_rT,
geneToModule = c(
"Root" = "Root",
"A" = "APC",
"B" = "TP53",
"C" = "KRAS",
"D" = "PIK3CA, NRAS",
"E" = "FBXW7, ARID1A",
"F" = "ATM, SMAD2",
"G" = "SOX9, SMAD4")) # Modules
In [3]:
## DAG of restrictions representation
plot(COADREAD_fitness, expandModules = TRUE, autofit = TRUE)
Map Genotypes to Fitness¶
In [24]:
## Evaluation of all possible genotypes fitness
## under the previous fitness specifications
COADREAD_FL <- evalAllGenotypes(COADREAD_fitness, max = 131072)
## Fitness landscape representation
plotFitnessLandscape(COADREAD_FL)
Simplified Model¶
In [26]:
## Restriction table, including five-modules DAG of
## restrictions specifications and associated fitness
COADREAD_rT_5d <- data.frame(parent = c("Root", "A", "B", "C"), # Parent nodes
child = c("A", "B", "C", "D"), # Child nodes
s = 0.5,
sh = c(rep(-1, 4)),
typeDep = "MN")
## Create fitness specifications from simplified DAG of restrictions
COADREAD_fitness_5d <- allFitnessEffects(COADREAD_rT_5d,
geneToModule = c( "Root" = "Root",
"A" = "APC",
"B" = "TP53",
"C" = "KRAS",
"D" = "PIK3CA, NRAS"),
drvNames = c("APC", "TP53", "KRAS",
"PIK3CA", "NRAS"))
In [3]:
## Simplified DAG of restrictions representation
plot(COADREAD_fitness_5d, expandModules = TRUE, autofit = TRUE)
Map Genotypes to Fitness¶
In [27]:
## Evaluation of all possible genotypes fitness under the previous fitness specifications
(COADREAD_FL_5d <- evalAllGenotypes(COADREAD_fitness_5d))
Map Genotypes to Fitness¶
In [28]:
## Fitness landscape representation
plotFitnessLandscape(COADREAD_FL_5d, use_ggrepel = TRUE)
Frequency-dependent fitness¶
Clones that coexist in a tumor can influence the fitness of each other in a frequency-dependent manner.
Frequency-dependent fitness (cont.)¶
In [29]:
## Mapping of genotypes to frequency-dependent fitness
# Not explicitly mapped genotypes are assigned a fitness of cero
COADREAD_gen_freqdep <- data.frame(
Genotype = c("WT", "APC","APC, TP53",
"APC, TP53, KRAS",
"APC, TP53, KRAS, PIK3CA",
"APC, TP53, KRAS, NRAS",
"APC, TP53, KRAS, PIK3CA, NRAS"),
Fitness = c("1", "1.5",
"2.25", "3.375", "5.0625", "5.0625",
"5.0625 - ((f_APC_TP53_KRAS_PIK3CA + f_APC_TP53_KRAS_NRAS))/2"),
stringsAsFactors = FALSE)
## Fitness specifications
COADREAD_fitness_freqdep <- allFitnessEffects(genotFitness = COADREAD_gen_freqdep,
frequencyDependentFitness = TRUE,
frequencyType = "rel")
Map Genotypes to Fitness¶
In [30]:
## Evaluate all genotypes considering population sizes of the clones
(COADREAD_FL_freqdep <- evalAllGenotypes(COADREAD_fitness_freqdep,
spPopSizes = c("WT" = 5, "APC" = 5, "APC, TP53" = 5,
"APC, TP53, KRAS" = 10,
"APC, TP53, KRAS, PIK3CA" = 50,
"APC, TP53, KRAS, NRAS" = 50,
"APC, TP53, KRAS, PIK3CA, NRAS" = 50)))
Map Genotypes to Fitness (cont.)¶
In [31]:
## Fitness landscape representation
plotFitnessLandscape(COADREAD_FL_freqdep)
Conclusions¶
Fitness landscapes include all possible paths of tumor progression and enable the study of different outcomes depending on the selected evolutionary model
We have mapped various cancer progression models (mutual exclusivity assumptions) to different evolutionary models and analyzed the resulting fitness landscapes
All this evidence supports the idea that cancer progression is better explained through an evolutionary perspective
Current cancer progression models cannot capture these phenomena and, thus, conclusions derived from them should be questioned
OncoSimulR is a very complete and convenient clone-based genetic simulator to evaluate cancer progression under evolutionary models, but is limited to:
- Small sets of genes for fitness landscapes interpretation.
- No fitness landscape for studying order of effects.
- Modules do not allow to define epistatic relationships between genes of the same module.
References¶
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